Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Kiselev, Alexei D.; Ali, Ranim; Rybin, A. V.

doi:10.3390/e23111409

Cited by 4 publications

(11 citation statements)

References 85 publications

(100 reference statements)

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“…Dynamics of entanglement for Gaussian type of states (sqeezed states, Schrodinger cat and etc.) can be considered in framework presented in [22]. However general approach for criterion of entanglement (including Fock states) requires the nearest separable state (e.g.…”

Section: Resultsmentioning

confidence: 99%

Algebraic approach for investigation of a multi-mode quantum system dynamics

Gaidash¹,

Kozubov²,

Kiselev³

et al. 2022

Preprint

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We introduce algebraic approach for superoperators that might be useful tool for investigation of quantum (bosonic) multi-mode systems and its dynamics. In order to demonstrate potential of proposed method we consider multi-mode Liouvillian superoperator that describes relaxation dynamics of a quantum system (including thermalization and intermode coupling). Considered algebraic structure of superoperators that form Liouvillian and their algebraic properties allows us to diagonilize multi-mode Liouvillian to find its spectrum. Also it allows to derive linear by mean number of thermal (environmental) photons approximation for time-evolution superoperator that keeps amount of considered dimensions in Fock space finite (assuming initial amount of dimensions finite) that might be helpful regarding entanglement dynamics problems. Conjugate Liouvillian is considered as well in order to perform analysis in Heisenberg picture, it can be implemented for multi-time correlation functions derivation.

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Section: Resultsmentioning

confidence: 99%

Algebraic approach for investigation of a multi-mode quantum system dynamics

Gaidash¹,

Kozubov²,

Kiselev³

et al. 2022

Preprint

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“…Our technique being directly applicable to quantum dynamics of continuous variables [22] might also provide a useful method to investigate Lindblad dynamics of the systems of coupled oscillators with P T symmetry previously studied in both classical [33,34] and quantum [35,36] regimes. The analytical approach can be readily extended to study a number of problems such as quantum dynamics of mixed polarization states transmitted in lossy quantum communication channels [37][38][39] and the problems related to controlled quantum dynamics in a realistic setup involving open environments.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of Characteristic and One-Point Correlation Functions of Multi-Mode Bosonic Systems: Exactly Solvable Model

2021

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In this communication we study dynamics of the open quantum bosonic system governed by the generalized Lindblad equation with both dynamical and environment induced intermode couplings taken into account. By using the method of characteristics we deduce the analytical expression for the normally ordered characteristic function. Analytical results for one-point correlation functions describing temporal evolution of the covariance matrix are obtained.

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“…As far as correlations are concerned, there is an extensive body of the literature dealing with dynamics of entanglement in open continuous-variable systems such as two coupled oscillators [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ] (see also Refs. [ 44 , 45 ] for reviews).…”

Section: Introductionmentioning

confidence: 99%

“…[ 44 , 45 ] for reviews). It turned out that the decay time of entanglement (the time of disentanglement) may be shorter than the time of decoherence and, under certain conditions, finite-time disentanglement commonly known as the “sudden death of entanglement” [ 46 , 47 , 48 , 49 , 50 , 51 ] may also take place in continuous-variable systems [ 33 , 39 , 43 ].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2.1 , our starting point is the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation (the general form of quantum kinetic equations which preserves the complete positivity of the dynamics [ 52 , 53 , 54 ]) for the multi-mode bosonic system interacting with the thermal bath and we, following Refs. [ 43 , 55 ], present its exact solution derived by solving the dynamical equation for the normally ordered characteristic function. In Section 2.2 , we deduce general formulas that characterize the temporal evolution of Gaussian states using the generalized two-point fidelity, the evolution speed and the covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

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Speed of Evolution and Correlations in Multi-Mode Bosonic Systems

Kiselev

Ali

Rybin

2022

Entropy

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We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert–Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

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Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

Cited by 4 publications

References 85 publications

Algebraic approach for investigation of a multi-mode quantum system dynamics

Algebraic approach for investigation of a multi-mode quantum system dynamics

Dynamics of Characteristic and One-Point Correlation Functions of Multi-Mode Bosonic Systems: Exactly Solvable Model

Speed of Evolution and Correlations in Multi-Mode Bosonic Systems

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